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  • A 'thermacole' icebox is a cheap and an efficient method for storing small quantities of cooked food in summer in particular. A cubical icebox of side 30 cm has a thickness of 5.0 cm.

Q. 11.17 A ‘thermacole’ icebox is a cheap and an efficient method for storing small quantities of cooked food in summer in particular. A cubical icebox of side 30 cm has a thickness of  5.0\; cm. If  4.0\; kg  of ice is put in the box, estimate the amount of ice remaining after 6 h. The outside temperature is 45^{\circ}C.and co-efficient of thermal conductivity of thermacole is  0.01\; j\; s^{-1}m^{-1}K^{-1}.  [Heat\; of\; fusion\; of\; water=335\times 103\; j\; kg^{-1}]

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Side of the box s = 30 cm

Area available for conduction A

A = 6s2

A=6(30)2

A=5400 cm2 = 0.54 m2

Temperature difference = 45 oC

Co-efficient of thermal conductivity of thermacole is k = 0.01 J s-1 m-1 K-1 

Width of the box is d = 5 cm

Heat absorbed by the box in 6 hours is \Delta Q

\\\Delta Q=\frac{kA\Delta T}{l}\\ \Delta Q=\frac{0.01\times 0.54\times 45\times 6\times 60\times 60}{0.05}\\ \Delta Q=104976\ J

Heat of fusion of water is L=335\times 10^{3}\ J\ kg^{-1}

Amount of ice which has melted is m'

\\m'=\frac{\Delta Q}{L}\\ m'=\frac{104976}{335\times 10^{3}}\\ m'=0.313\ kg

Amount of ice left after 6 hours = 4 - 0.313 = 3.687 kg

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